As an exhaust apparatus of an internal combustion engine to be used by an automotive vehicle, there has so far been known an exhaust apparatus as shown in FIG. 18 (for example see Patent Document 1). In FIG. 18, the known exhaust apparatus 4 is constructed to allow an exhaust gas to be introduced therein, after the exhaust gas is exhausted from an engine 1 serving as an internal combustion engine and then passes through an exhaust manifold 2 and a catalytic converter 3 where the exhaust gas is purified.
The exhaust apparatus 4 is constituted by a front pipe 5 connected to the catalytic converter 3, a center pipe 6 connected to the front pipe 5, a main muffler 7 connected to the center pipe 6 and serving as a sound deadening device, a tail pipe 8 connected to the main muffler 7, and a sub-muffler 9 interposed to the tail pipe 8.
As shown in FIG. 19, the main muffler 7 has an expansion chamber 7a for introducing therein through small through bores 6a formed in the center pipe 6 to expand the exhaust gas to mute the sounds of the exhaust gas, and a resonance chamber 7b allowing a downstream open end 6b of the center pipe 6 to be received therein. The sound of the exhaust gas introduced into the resonance chamber 7b from the downstream open end 6b of the center pipe 6 has a specified frequency, and thus can be muted by the Helmholtz resonance.
It is here assumed that the length of the center pipe 6 projecting into the resonance chamber 7b from the small through bores 6a is L1, and the cross section area of the center pipe 6 is S, the volume of the resonance chamber 7b is V, and the sound speed in the air is C. At this time, the resonance frequency fn in the air can be obtained by the following equation (1) based on the Helmholtz resonance.
                              f          n                =                              c                          2              ⁢              π                                ⁢                                    S                              V                ·                                  L                  1                                                                                        (        1        )            
As clearly understood from the above equation, the resonance chamber is designed to enable its resonance frequency to be tuned to the low frequency side by increasing the volume V of the resonance chamber 7b or otherwise by lengthening the length L1 of the center pipe 6 projecting into the resonance chamber 7b, while enabling its resonance frequency to be tuned to the high frequency side by decreasing the volume V of the resonance chamber 7b or otherwise by shortening the length L1 of the center pipe 6 projecting into the resonance chamber 7b. 
The sub-muffler 9 is adapted to suppress the sound pressure level of the air column resonance from being increased when the air column resonance is generated in response to the pipe length of the tail pipe 8 in the tail pipe 8 by the pulsation of the exhaust gas during the operation of the engine 1.
In general, the pipe having an upstream open end and a downstream open end at the respective upstream and downstream sides of the exhaustion direction of the exhaust gas is subjected to incident waves caused by the pulsation of the exhaust gas during the operation of the engine 1 at the upstream open end and the downstream open end, thereby generating an air column resonance. The air column resonance has a frequency corresponding to a half wavelength equal to the pipe length of the tail pipe as a basic component, and thus has wavelengths obtained by multiplying the half wavelength by natural numbers.
For example, taking an example in which the tail pipe 8 having no sub-muffler 9 extends backwardly from the main muffler 7, as shown in FIG. 18, the wavelength λ1 of the air column resonance of a basic vibration (primary component) is roughly double the pipe length L of the tail pipe 8, while the wavelength λ2 of the air column resonance of the secondary component is roughly one time the pipe length L of the tail pipe 8 as shown in FIG. 20. The wavelength λ3 of the air column resonance of the third component is ⅔ times the pipe length L of the tail pipe 8. Therefore, the tail pipe 8 has therein standing waves having respective nodes of sound pressures at the upstream open end 8a and the downstream open end 8b. 
The frequency of the air column resonance “fc” can be represented by the following equation (2).f c=(c/2L)·n   (2)
c: sound speed, L: pipe length of tail pipe, n: degree
As it is obvious from the above equation (2), it is known that the longer the pipe length L of the tail pipe 8, the more the air column resonance frequency “fc” is transferred to the low frequency area, thereby causing the exhaust gas sounds to be increased at the low rotation time of the engine 1, and thereby causing exhaust gas noises to be deteriorated and giving unpleasant feelings to a driver.
In particular, as shown in FIG. 21, when the primary component f1 and the secondary component f2 of the air column resonance are generated in the normal rotation area of the engine 1, there is generated unpleasant noises called muffled sounds which are a cause for the exhaust gas noises to be deteriorated.
For this reason, in the case of the pipe length of the tail pipe 8 being long, the sub-muffler 9 smaller in capacity than the main muffler 7 is provided at the optimum position among the abdominal portion of the standing wave high in the sound pressure level, and the respective abdominal portions of the primary component f1 and the secondary component f2 of the exhaust gas sounds caused by the air column resonance, so that the exhaust gas noises are suppressed in the normal rotation area of the engine 1 to prevent the unpleasant feeling from being given to the driver.
On the other hand, it may be considered that the exhaust apparatus 4 is provided with no sub-muffler 9 to reduce its production cost and its weight, however, no sub-muffler 9 provided on the exhaust apparatus 4 leads to lengthening the length of the tail pipe 8, and thus to the frequency of the air column resonance of the tail pipe 8 moving toward the low frequency side.
In this case, it may be considered that the frequency of the air column resonance of the resonance chamber 7b of the main muffler 7 connected with the upstream open end 8a of the tail pipe 8 is tuned to the frequency of the air column resonance of the tail pipe 8, thereby muting the air column resonance of the tail pipe 8 in the resonance chamber 7b of the main muffler 7.
More specifically, it may be considered that in accordance with the equation (1), the resonance chamber is designed to enable the resonance frequency of the resonance chamber 7b to be tuned to the low frequency side by increasing the volume V of the resonance chamber 7b or otherwise by lengthening the length L1 of the center pipe 6 projecting into the resonance chamber 7b, thereby preliminarily muting the air column resonance generated in the tail pipe 8 in the resonance chamber 7b. 